Python Program for How to Check if a Given Number is Fibonacci Number or Not

In this tutorial, we will learn how to check if the given number is a Fibonacci number or not.

Here, we have a number "n", and we have to check if it is a Fibonacci number. Starting number of Fibonacci series are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on.

Example:

Input number: 5
Output: Yes, the given number is a Fibonacci_Number.

Input number:  22
Output: No, the given number is not a Fibonacci_Number.

Input number: 55
Output: Yes, the given number is a Fibonacci_Number.

We can also use the following property of the Fibonacci number for checking if the given number is a Fibonacci number or not:

A number is Fibonacci number only if one of (5 * R * R + 4) or ( 5 * R * R - 4) or both of them are the perfect square.

Python Program to Check if Given Number if Fibonacci or Not:

import math as m
 
# Here, we will create a utility function that will return true if K is a perfect square
def is_Perfect_Square(K):
    s = int(m.sqrt(K))
    return s * s == K
 
# Now, we will create a function which will return "true" if R is a Fibinacci Number, 
# else it will return "false"
def is_Fibonacci(R):
 
    # R is a Fibinacci number only if one of (5 * R * R + 4) or (5 * R * R - 4) or both 
   # of them are perferct square
    return is_Perfect_Square(5 * R * R + 4) or is_Perfect_Square(5 * R * R - 4)
    
# Now, we will create a utility function for testing the above functions
for J in range(1, 22):
     if (is_Fibonacci(J) == True):
         print ("Number:", J, ": Yes, the given number is a Fibonacci_Number")
     else:
         print ("Number:", J, ": No, the given number is not a Fibonacci_Number")

Output:

Number: 1 : Yes, the given number is a Fibonacci_Number
Number: 2 : Yes, the given number is a Fibonacci_Number
Number: 3 : Yes, the given number is a Fibonacci_Number
Number: 4 : No, the given number is not a Fibonacci_Number
Number: 5 : Yes, the given number is a Fibonacci_Number
Number: 6 : No, the given number is not a Fibonacci_Number
Number: 7 : No, the given number is not a Fibonacci_Number
Number: 8 : Yes, the given number is a Fibonacci_Number
Number: 9 : No, the given number is not a Fibonacci_Number
Number: 10 : No, the given number is not a Fibonacci_Number
Number: 11 : No, the given number is not a Fibonacci_Number
Number: 12 : No, the given number is not a Fibonacci_Number
Number: 13 : Yes, the given number is a Fibonacci_Number
Number: 14 : No, the given number is not a Fibonacci_Number
Number: 15 : No, the given number is not a Fibonacci_Number
Number: 16 : No, the given number is not a Fibonacci_Number
Number: 17 : No, the given number is not a Fibonacci_Number
Number: 18 : No, the given number is not a Fibonacci_Number
Number: 19 : No, the given number is not a Fibonacci_Number
Number: 20 : No, the given number is not a Fibonacci_Number
Number: 21 : Yes, the given number is a Fibonacci_Number